Relationship between Maxwell Matrix and Spice Matrix for 2D Extractor

Because there are two different expressions for the same thing, the entries of the Maxwell matrix and Spice capacitance matrices can relate to each another.

Matching the coefficients of the voltages results in:

(1)C^M_i,i = C^S_i,0 + C^S_i,1 + C^S_i,2 + ... + C^S_i,N-1

(2)C^M_i,j = - C^S_i,j (for i not equal to j)

So the off-diagonal entries of the Maxwell capacitance matrix (which are generally negative) are the opposite of the off-diagonal entries of the Spice capacitance matrix (which are positive.) And the main-diagonal entries of the Maxwell matrix are the sum across an entire row of the Spice capacitance matrix.

Alternatively, you could express the grounded capacitor in the Spice matrix as the sum across a whole row of the Maxwell capacitance matrix:

C^S_i,0 = C^M_i,1 + C^M_i,2 + ... + C^M_i,N